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3 years ago

Abby is constructing the inscribed circle for △JKL .

Mathematics

2 answers:

Nady [450]3 years ago

5 0

Just took quiz. Correct answer is B

alex41 [277]3 years ago

3 0

Answer:

Hence, the correct answer is:

Construct the angle bisector of ∠J .

Step-by-step explanation:

The steps for the construction of inscribed circle are:

Bisect one of the angles

Bisect another angle

Where they cross is the center of the inscribed circle, called the incenter

Construct a perpendicular from the center point to one side of the triangle

Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle!.

The answer that best suits the construction among the given option is:

Construct the angle bisector of ∠J.

(Since first steps of the construction will be satisfied)

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3 years ago

Complete the identity. 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

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In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

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Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

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Step-by-step explanation:

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